Software: First and foremost: must be unix-like, must be able to communicate in both ways with an open-wrt router firmware distro and the devices on the local network (android, windows, linux, ipadOS systems). Must be very secure, like enterprise-grade or almost like that. Must be free and open-source. Must be somewhat fault-tolerant (so no Arch or gentoo or anything like that, i don't feel like recompiling the server's system daily). Must have these in base repos or easily installed in other methods: secure ssh client (like openSSH or such caliber), a software that enables me to securely control and see the gui of the server from android (Rustdesk? or such), (optionally i2p, dnscrypt, vpn clients, not needed if the router has them, just in case of emergency), ip camera management software, high-security intrusion-detection system, https server with css and js support (preferably command-line). Window manager: must support a very easy to use and lightweight tiling window manager (like i3wm) or if not, its installation and configuration needs to be possible and documented.
Hardware: affordable, x86_64 architecture, should be able to handle all of these at the same time, without freezing or overheating (i live in Hungary, so should be able to handle up to 40°C air temperature with stock fans or there should be space for more fans. liquid cooling is no-go).
I have considered these operating systems. Are any of these bad ideas? What you recommend that is not here?
AlmaLinux
Alpine Linux
Ubuntu Server
Rhino Linux (unofficial ubuntu rolling)
Debian Testing
Void Linux
FreeBSD
i have all of those things on my ubuntu server; but i wouldn't characterize all of them as enterprise-grade . my ubuntu server it's based off of off-the-shelf hardware from a couple years ago and it does all of those things that you described plus more.
it's my wifi router; my data storage backup; my home made security system; my media server inside; & my cat's favorite warm spot all within a tiny case the size of a toaster with lots of harddrives. it uses 2 kvm/qemu based virtual machines on top of the bare iron and they both use pci-passthrough; the first virtual machine is based off of the pfsense soft firewall & router and also serves to air-gap the bare iron server from the internet and the second virtual machine is windows 10 and serves to provide wifi 6 & 7 speeds with the windows ap driver.
i wouldn't describe any of it as enterprise grade since they're a bit hacky: for example, the server is mostly headless; but i did install the xserver & vnc because i use the motion project along with a bunch of old androids to create a homemade security monitoring system and that requires a browser. this means that i can now access the server's gui anywhere than i want; but it's subject to vnc's limitations.
however the things that come from the soft firewall are definitely enterprise grade: the vpn works well and i can use both it and ssh from anywhere in the world to access my home network and i could theoretically add in a remote check in capability from a new project that reacts to incoming connections.
the only thing i don't think it could do i the high temperatures; the case is compact so i doubt that its thermals are any good.
so i should avoid mini and compact pcs then, right?
for heat: you're either going to want a blade serve with lots of fans or big, mostly empty case.